Problem: Rewrite as a simplified fraction. ${0.9\overline{71} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 971.7171...\\ 10x &= 9.7171...\end{align*}}$ Subtracting the two equations, we have: ${990x = 962}$ ${x = \dfrac{962}{990}} $ ${x = \dfrac{481}{495}} $